Linear error correcting codes and their application in DNA analysis

Abstract

The application of various areas of the theory of coding in the problems of analysis of the genome includes different areas. For instance, the method for detecting linear block codes, which takes into account possible insertions and divisions in DNA sequences. For a lot of such problems, we shall consider the number of codes of the required dimension. One of the most important such tasks is counting their number. We study this area it in this paper. We solve the problem of defining the number of cyclic codes over finite field with two arbitrary fixed parameters. These parameters are n, i.e., the length of the code, and k, i.e., the number of information symbols. The algorithm to solve this problem in general is described in this paper. Also the results at some fixed values are given. We have counted some constants connected with coding theory, which can be used in some problems of genome analysis.